The average age of a group is increased by 6 years when a person whose age is 24 years is replaced by a person whose age is 66. Find the number of persons in the group.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 7.
Average = Sum of observations/Number of observations
Let, the number of people in the group is x and their previous average be y
The previous sum of the ages of the group = xy
When a person of age 24 years is replaced by a person of the age of 66 years
The sum of the ages of the new group = xy - 24 + 66
The new average = y + 6
The sum of the ages of the new group = xy + 6x
⇒ xy - 24 + 66 = xy + 6x
⇒ 6x = 42
⇒ x = 7
Thus, the number of persons in a group is 7